Abstract
A statistical procedure for the analysis of time-frequency noise maps is presented and applied to LISA Pathfinder mission synthetic data. The procedure is based on the Kolmogorov-Smirnov like test that is applied to the analysis of time-frequency noise maps produced with the spectrogram technique. The influence of the finite size windowing on the statistic of the test is calculated with a Monte Carlo simulation for 4 different windows type. Such calculation demonstrate that the test statistic is modified by the correlations introduced in the spectrum by the finite size of the window and by the correlations between different time bins originated by overlapping between windowed segments. The application of the test procedure to LISA Pathfinder data demonstrates the test capability of detecting non-stationary features in a noise time series that is simulating low frequency non-stationary noise in the system.
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Notes
w is assumed to be square normalized to 1 so that \(\sum _{i} {w_{i}^{2}} = 1\).
Critical values are cut-off values that define regions where the test statistic has a probability lower than α to be if the null hypothesis is true. α is the significance level such that the confidence level is 1−α. The null hypothesis is rejected if the test statistic lies within this region which is often referred to as the rejection region [10].
The expected model was obtained by a fit procedure of a sample spectra realized with all the noise sources kept stationary at their nominal values.
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This research was supported by the Centre National d’Études Spatiales (CNES).
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Ferraioli, L., Armano, M., Audley, H. et al. Kolmogorov-Smirnov like test for time-frequency Fourier spectrogram analysis in LISA Pathfinder. Exp Astron 39, 1–10 (2015). https://doi.org/10.1007/s10686-014-9432-z
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DOI: https://doi.org/10.1007/s10686-014-9432-z